Intermodulation
Intermodulation
Performance and Measurement of Intermodulation
Components
by Lloyd Butler
First published in "Amateur Radio" August 1997
Introduction
To define the performance of a receiver or transmitter, various
specifications are recorded which are obtained from measurements
carried out. Perhaps the least understood of these in amateur radio
circles is intermodulation performance and how it is measured. The
aim of this article is first to discuss intermodulation products
and how they are produced and then look at how they are defined and
What are Intermodulation Products?
When a single frequency (f1) is fed through a device whose
output is not a linear function of its input, harmonics of f1 are
generated, i.e. 2f1, 3f1, 4f1, 5f1, etc (no device is perfect and
so harmonics are always generated even at low levels).
Now, if two separate frequencies exist together in a non-linear
device, sum and difference frequencies are also produced in
addition to the harmonics. This can be shown mathematically to be
the result of a multiplication process between the two original
frequencies and hence the two new frequencies are called products.
If the two original frequencies are f1, f2 and the highest
frequency is f2, then we can expect two other components (or
products) of (f1+f2) and (f2-f1). However, it doesn't stop there.
Since there are harmonics of f1 and f2, then there will be sum and
difference products between all of the harmonics and the
fundamentals and between each other. These are the intermodulation
products which are frequency components distinct from the harmonic
components discussed in the previous paragraph. Of course, if there
are more than two fundamental frequencies, then the multitude of
products is compounded further.
It can be shown, using a mathematical series, that when
harmonics are generated, the harmonies extend upward in frequency
to approach infinity, progressively decreasing in amplitude as the
frequency increases. Likewise, the intermodulation products could
also be considered to be infinite in number. However, we are only
really interested in those of practical significance, that is of
such a level that they might deteriorate the quality of our signal
beyond an acceptable level.
To examine intermodulation products we will consider two
frequencies f1 and f2 and some of the orders of intermodulation
products. To define the order, we add the harmonic multiplying
constants of the two frequencies producing the intermodulation
product. For example, (f1+f2) is second order, (2f1-f2) is third
order, (3f1-2f) is fifth order, & etc. Let's consider f1 and f2
to be two frequencies of 100 kHz and 101 kHz respectively, that is
1 kHz apart. We now prepare Table 1 showing some of the
intermodulation products.
Looking carefully at the table, we see that only the odd order
intermodulation products are close to the two fundamental
frequencies f1 and f2. One third order product (2f1-f2) is 1 kHz
lower in frequency than f1 and another (2f2-f1) I) is 1 kHz above
f2. One fifth order product (3f1-2f2) is 2 kHz below f1 and another
(3f2-2f1) is 2 kHz above f2. In fact it is the odd order products
which are closest to the fundamental frequencies f1 and f2.
Let's expand further the odd order products as shown in Table
The series of odd order products can be seen to descend and
ascend progressively in increments of 1 kHz from the two
fundamental frequencies f1 and f2 respectively. A typical spectrum
produced could be depicted as shown in the chart of Figure 1.
Figure 1 - Spectrum of Intermodulation Components
Of all the harmonics and intermodulation components produced,
are often only interested in those which fall in. the passband of
our equipment and, in the case of the intermodulation components,
those which happen to be closest to our fundamental frequencies.
The third order components are the closest and also usually the
highest in amplitude. Because of this, they are usually the
products of most concern and are those which are commonly measured
and defined in transmitter and receiver performance
specifications.
Effects of lntermodulation Components
The existence of intermodulation components affects the
performance of equipment in various ways. First let's look at audio
amplifiers. The presence of any component at the output of an
amplifier, but not fed into it, degrades the quality of the signal
being amplified. We call this distortion, which can be the result
of non-linearity in the amplifier causing the generation of
harmonics of the signal frequencies and, in turn, intermodulation
components. So we have harmonic distortion and intermodulation
distortion which can individually be defined. We often see
intermodulation distortion abbreviated to IMD.
Some different effects can be experienced when non-linearity
exists at RF in a transmitter and, in particular, in the final
linear amplifier of the transmitter. Consider the amplifier
delivering sideband components to the antenna at radio frequencies
and because of nonlinearity, harmonics of the various sideband
components are generated plus various intermodulation, components.
The harmonic components and the even order intermodulation
components will be well spaced away from the operating frequency,
and hopefully attenuated by the tuned amplifier tank circuit and
the antenna tuning system. Not so for the odd-order intermodulation
components which are closely spaced around the fundamental
components from which they were generated. First of all they will
show up as audio distortion after being received and detected by
the radio receiver. However, that's not all! We have seen from the
previous paragraphs that the odd order components spread out either
side of the fundamental components in progression gradually
decreasing in amplitude. The effect is to broaden the radiated
signal and in receiving the signal, we experience the familiar
sideband splatter. As most of us well know, this causes
interference to others trying to use another channel near in
frequency.
Another application where those odd order, intermodulation
components are of considerable concern is in the first Mixer stage
of a superheterodyne receiver. The special function of the mixer
stage is to produce some form of non-linearity so that an
intermediate lower frequency is formed from the sum or difference
between the incoming RF signal frequency and a local oscillator
frequency. The mixer stage is, therefore, a prime spot for other
intermodulation products which we might not want. Let's look at an
example. Our receiver is tuned to a signal on 1000 kHz but there
are also two strong signals, f1 on 1020 kHz and f2 on 1040 kHz. The
nearest of these (f1) is 20 kHz away and our sharp intermediate
frequency (IF) stage filter of 2.5 kHz bandwidth is quite capable
of rejecting this signal. However, the RF stages before the mixer
are not so selective and the two signals f1 and f2 are seen at the
mixer input, free to produce intermodulation components at will.
Now work out the third order intermodulation component (2f1-f2) and
we get (2x ) = 1000 kHz, right on our signal frequency.
This is just one example of how intermodulation components or
out-of-band signals can cause interference within the working
Another form of interference in receivers which results from the
mixing of intermodulation components is Cross Modulation. This
becomes more apparent when dealing with AM signals and the
modulation on a strong out-of band signal transfers itself across
to modulate the signal being received. The process is probably
complex but, due to non linearity in the receiver, one can well
imagine the carrier and sideband frequencies of the out-of-band
modulated signal mixing to produce difference second-order
components at the audio frequencies of modulation. Due to the same
non-linearity, the unwanted audio components intermodulate the
signal being received. If the receiver is designed for good
intermodulation immunity, it will also have good cross modulation
Receiver IMD Performance
To assess the receiver for its tolerance against interference
from internally generated intermodulation products, the receiver is
tested for its sensitivity to third-order products using two equal
level signals fed to its input and typically 20 kHz apart. The
receiver is tuned to the frequency of one of the third order
products derived from the two signal frequencies. The level of the
combined signals at the input is adjusted until the detected output
level is equal to that generated by the receiver's self noise. That
is, there is a 3 dB change in output level between when the signals
are on and when they are off. The level of the third order product
necessary to produce output equal to the receiver "noise floor is
recorded. For the purposes of following discussion we will call
this level IMD Threshold.
We also need to know the normal signal input level which
produces audio output equal to that of the receiver's own inherent
noise or its noise floor. This is done by tuning the receiver: to
one of the two frequencies and again adjusting input level to give
an output level 3 dB above the noise output level. For the purposes
of the discussion we will record this input level as the Signal
Threshold. The difference in dB between the IMD threshold and the
signal threshold is called the Intermodulation Dynamic Range or IMD
Dynamic Range. The higher the difference, the better the immunity
to interference from IMD products.
Now, there is an important characteristic of the third-order
products which makes their presence more of a problem than one
might first imagine. Assuming no compression (due to AGC, etc),
output from a fundamental signal is proportional to input, ie for
10 dB rise in input level there is 10 dB rise in output level.
However, the output of the third order product is proportional to
the cube of signal input level and, for a 10 dB change in input
level, the product increases by 30 dB.
Now refer to Figure 2. One curve plots a linear rise in output
level against input level for the fundamental signal frequency. The
other plots the level of third-order IMD products against input
level, the output rising 30 dB for every 10 dB change in input
level. At an output level equal to the noise floor, the two curves
are separated by an input level difference equal to the IMD Dynamic
Range. As the intermodulation curve rises with greater slope than
the fundamental curve, they cross at a point called the Third-Order
Intercept Point where the intermodulation product output level is
equal to the fundamental signal output level.
Figure 2 - Receiver Intermodulation Performance Curves
The Third-Order Intercept point is normally a theoretical point
well above the receiver overload level. However, it is often
specified to define intermodulation levels, and particularly in
specifications for mixer packages.
The Third-Order Intercept point can be derived on decibel scales
by first extending the signal curve linearly from the signal
threshold point on the noise floor axis so that output level
increase in dB equals input level increase in dB. Mark the IMD
threshold point on the noise floor axis. This is at an input level
higher than signal threshold by an amount equal to the IMD dynamic
range. Mark another point on the noise floor axis beyond the IMD
threshold point by an amount equal to half the IMD dynamic range.
Extend this point vertically to cross the signal curve and this is
the Third-Order Intercept point. Join this point to the IMD
threshold point to complete the curves such as is shown in Figure
2. In the diagram, the noise floor input level is -120 dBm, the
third order components become detectable at 40 dBm and the IMD
dynamic range 80 dB. The theoretical third-order intercept occurs
at an input level of 120 dB above the noise floor input level.
It can be seen from the curves of Figure 2 that, above the IMD
threshold level, the IMD products can become quite a problem. In
the example, IMD products from out-of-band signals at an input
level of -40 dBm would barely be apparent. Increase the level by a
mere 10 dB and the interference from these products would increase
Receiver Measuring Gear
To carry out intermodulation performance on a receiver, the
set-up shown in Figure 3 is required. The RF outputs of two signal
generators are combined in a hybrid circuit designed to prevent
interaction between the two generators. A hybrid circuit is
balanced so that a signal at any one input port cannot reach the
other. However, both signals appear combined at an output port.
Figure 3 - Testing of Receiver for Third -order Intermodulation Performance
The combined output is fed to the receiver via an adjustable
attenuator with a range up to around 80 dB and resolution of 1 dB.
Assuming that the receiver has an input resistance of 50 ohms, both
the combiner and attenuator are designed for a circuit impedance of
A hybrid combiner and attenuator assembled by the writer is
shown in Figure 4. The hybrid circuit, Figure 5, is one taken from
the ARRL Handbook. The combiner has an insertion loss of 6 dB for
each signal channel.
Figure 4 - Hybrid Combiner and 50 ohm Attenuator assembled by VK5BR
Figure 4 -Hybrid Combiner
The attenuator was made up using two mechanically interlocking,
in-line switch assemblies of the type similar to those used in
older style push-button car radios. The assemblies, each of six
switches, were recovered from some old intercom units and each
switch came with plenty of change/over contacts to switch in or out
an attenuation pad. One assembly switches in 1 dB, 2 dB, 3 dB, 5
dB, 10 dB and 15 dB pads. The other switches in 10 dB, two of 20 dB
and 25 dB pads. Up to three switches on each assembly can be
simultaneously pressed to lock in so that up to six pads can be in
circuit together to provide a continuous selection of total
attenuation between 1 and 95 dB. The circuit diagram of the
complete attenuator is shown in Figure 6.
50 Ohm Attenuator
Figure 6 -Simplified Circuit Diagram of the 50 ohm Attenuator
The only other device necessary is some form of AC voltmeter to
measure the comparative level of audio signal at the receiver
output. All it is required to do is to record a 3 dB change in
level above the receiver noise floor. In terms of voltage increase,
this is a rise of 1.4 times.
Our references have so far been made to levels in dBm, or
decibels referred to one milliwatt. However, signal generator
outputs are commonly calibrated in microvolts and millivolts with
scales in multiples of 10. To convert between units, 1uV across 50
ohms is - 107 dBm. Each time the voltage is multiplied by 10, add
20 dB so that 10uv is 87 dBm, 100 uV is -67 dBm, etc.
To find the signal threshold, set one signal generator to a
fairly low level (say 10uV or -87 dBm) and tune the receiver to the
signal generator frequency. Adjust the attenuator so that the
signal raises the audio output signal just 3 dB (1,4 times volts)
above the noise level (measured with signal off). The signal
threshold in dBm is equal to -87 dBm, minus the loss in dB set by
the attenuator, minus 6 dB loss in the hybrid combiner.
To find the third-order IMD threshold, set the two generators
(20 kHz apart in frequency) to an equal level somewhat higher, such
as 10 mV (-27 dBm). Tune the receiver to the frequency of one of
the third-order products. Adjust the attenuator until the audio
output from the third-order signal is just 3 dB above the noise
level. The IMD threshold is equal to -27 dBm, minus the loss in dB
set by the attenuator, minus 6 dB loss in the hybrid combiner.
Transmitter Tests
To check out a single-sideband transmitter for those
intermodulation components which cause sideband splatter, we need a
two tone audio generator to feed into the microphone input of the
transmitter. This can be quite a simple test unit, consisting of
two fixed frequency oscillators delivering the same output level
into a resistive network which combines the two signals. Simple two
tone generators have been presented in Amateur Radio from time to
time. In the March 1983 issue, the writer described one using two
FX205 Tone Generator packages. In this one, frequencies were set at
1000 Hz and 1600 Hz.
Figure 7 - SSB transmitter test arrangement for IMD performance
A test arrangement for the transmitter is shown in Figure 7. The
two tone oscillator level is adjusted to provide full RF power from
the transmitter into a dummy load. Power can be monitored with the
usual Power/SWR meter. Apply the audio signal in short bursts as
most single-sideband transmitters are designed for speech and the
final amplifier stage might be damaged if sustained on continuous
full power. The best way to monitor the level of the various
intermodulation sideband components is to examine the RF output
signal using a Spectrum Analyser.
Figure 8 - Typical Spectral display from the RF output of a SSB transmitter using two tone modulation and showing the intermodulation products generated (sample from ARRL test in March 1996 issue of QST).
Figure 8, taken from March 1966 issue of QST, is a typical
spectrum analyser display of the RF output of a single-sideband
transmitter fed with two audio tones 1000 Hz apart. Two fundamental
RF sideband frequencies are created but we can also see a family of
odd-order intermodulation frequencies, either side of the two
fundamentals with all frequencies spaced 1000 Hz apart. The display
shows that the third order products are around 21 dB below the
fundamentals, the fifth order 30 dB below, the seventh order 33 dB
below, & etc., in decreasing amplitude as the order
progresses.
Whilst the spectrum analyser is the order of the day in the
modern electronics laboratory, not many radio amateurs could boast
of one in the radio shack. However, the Cathode Ray Oscilloscope
(CRO) is a more common piece of test gear, and with this we can get
some idea of whether there might be an excessive spread of
intermodulation sideband components. Figure 9, taken from the ARRL
Handbook, shows CRO displays of the RF output generated from a two
tone audio source fed to the transmitter. In diagram A, the
waveform is quite good and we could expect a fairly clean signal
transmitted. In diagram B, compression of the waveform peaks is
occurring, possibly because the final amplifier is being driven too
hard into a state of poor linearity. If there is poor linearity,
then we can expect intermodulation components to be generated and
sideband splatter.
Figure 9 - SSB Two Tone test showing RF waveform on a CRO (a) Good waveform (b) Peaks compressed (IMD high, sideband splatter).
Another test that might be applied is to demodulate the
transmitter so that we get the two tones back as audio. Perhaps a
station receiver can be used for this purpose if it can be
prevented from being overloaded by the transmitter. The audio
intermodulation distortion tests as described in the following
paragraphs can then be carried out. The tests could apply to any
mode of transmitter and matching receiver whether it be SSB, AM, or
FM (for AM, a simple rectifier and RF filter would be adequate for
demodulation). The only problem with this form of test is that the
distortion measured is the combined distortion of both transmitter
and receiver. If excessive distortion occurred, one would have to
be certain that it wasn't caused by the receiver.
Measurement of Intermodulation Distortion at Audio
Frequencies
As with other tests described, two audio signals at different
frequencies are fed through the device to be tested and the output
is monitored. If a modern spectrum analyser is available, the
relative amplitudes in decibels from all components at the output
can be displayed. As the X axis of the analyser display is
calibrated in frequency, the various intermodulation components can
be identified and their amplitudes recorded relative to the two
fundamental frequencies.
Another instrument of a past era, but which can do a similar
job, is the Heterodyne Wave Analyser. This is, in effect, a sharp
tuneable filter which achieves its sharpness and tuneability by
heterodyning the measured signal with a tuneable oscillator and
passing the difference frequency through a sharp fixed 50 kHz
crystal filter. By adjusting the tuneable oscillator, the various
frequency components can be selectively tuned in and the outputs at
50 kHz can be compared. The Wave Analyser was described in the
writer's previous article on Measurement of Distortion, Amateur
Radio June 1989.
Another method to measure the intermodulation level is to make
use of a CRO display as shown in Figure 10. Two audio signals of
widely different frequency are combined and fed into the device
under test. The lower frequency signal has an amplitude four times
that of the higher frequency signal. The output of the device is
fed to the CRO vertical plates via a high pass filter which removes
the low frequency signal. The CRO time base is externally
synchronised to the low frequency signal. Intermodulation is shown
on the display as an amplitude modulation waveform of the lower
frequency on the higher frequency carrier. The reason for the four
to one signal amplitude ratio is to amplify the apparent modulation
and improve resolution in reading the display. The test set-up,
shown in Figure 10, uses a 100 Hz low frequency signal and a 2000
Hz high frequency signal. A simple resistive mixing network is used
to prevent interaction between the audio generators. Referring to
Figure 11, percentage intermodulation is calculated from a and b
scaled on the CRO display as: % Intermod = (a-b)/2(a+b) x 100.
Figure 10 - Test for audio intermodulation distortion using CRO display.
In this test, it should be clear that we are essentially
measuring the effect of the second-order intermodulation components
at (f2-f1) 1900 kHz and (f2+f1) 2100 kHz. This should not be
confused with the fact that at radio frequencies we had been mainly
concerned with the odd-order products because it was those which
appeared in close to our tuned band. However, at audio frequencies,
both odd and even products fall within the audio band.
Figure 11 - CRO display waveform of intermodulation and method of measurement
Intermodulation products have been discussed with particular
attention to how their presence affects our transmitter and
receiver circuitry. In audio circuits, they are one of the
contributing distortion factors which deteriorate audio
reproduction quality. At radio frequencies in transmitters, they
appear as what we recognise as sideband splatter. In receivers,
circuits susceptible to intermodulation encourage interference from
signals outside the receiver pass-band.
Various ways have been explained as to how intermodulation
components can be measured and how the equipment performance in
terms of IMD susceptibility can be specified. The reason why the
third order performance is usually defined in RF circuits has also
been discussed.
References
1. Lloyd Butler VK5BR: Measurement of Distortion - Amateur
Radio, June 1989.
2. ARRL Handbook 1989: Chapter 25 Test Equipment &
M Chapter 18 - Voice Communications.
3. Jon Dyer G40BU.. High Frequency Receiver Design - Radio and
Electronics World, July 1983.
4. Lloyd Butler VK5BR: A Discussion on Mixers -Amateur Radio,
April 1988.
5. Lloyd Butler VK5BR: Two Tone Test Oscillator for SSB -
Amateur Radio, March 1983.